(where \(A\)  denotes the area of the event horizon) together with the ADM mass,The same results can be derived using the phase space formalism or the counterterms methods; see
[1]}, [2]} and [3]}. according to Ref. [4]}.
It follows that, for the flat black hole solution we obtain
\(S_{\text{fBH}} =& \frac{\pi ^2 p\: r_{+}^2}{2q} \ , \\ T_{\text{fBH}}=& -\frac{K\kappa a_{N} q^2 }{16 \pi r_{+}} - \frac{\Lambda r_{+}}{4\pi } \ , \\ M_{\text{fBH}}=& \frac{p\pi }{4q}m = -\frac{p\pi r_{+}}{48q}\left(3 K\kappa a_{N} q^2 + 4 \Lambda r_{+}^2\right) \ .\) 
